# Why does an increase in temperature lead to an increase in dipole oscillation?

As far as I know, heat radiation is caused by the electromagnetic waves produced by the permanent or induced dipoles of the heated material. The higher the heat, the higher the frequency of oscillation and as such, the higher the frequency of the electromagnetic waves. My question is, why do the molecules oscillate at a higher frequency when exposed to higher temperatures?

• Are you familiar with Equipartition theorem? Temperature is essentially the measure of how much vibration the molecule is showing (in this case)
– Cryo
Jan 4, 2021 at 9:15
• No, not familiar with this theorem, but I will check it out @Cryo, thanks Jan 4, 2021 at 9:33

The equation that relates the oscillating "angular speed" $$\omega$$ of a simple harmonic oscillator (i.e. a given molecule) to its energy of oscillation is $$E = \frac{1}{2}m\omega^2 x_0^2$$ where $$x_0$$ is the amplitude (max. displacement) of oscillation, and $$m$$ is the oscillator's mass. The mass of the oscillator will not (appreciably) change when it oscillates with more energy, as nothing is really happening to the molecule. $$x_0$$ will not change significantly, given that the molecule is surrounded by neighbors in some larger structure, like a solid or liquid. As such, the only element of its oscillation that can change is $$\omega (= 2\pi f)$$ - its angular speed (proportional to its frequency) - such that it oscillates faster.